Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27133285 | C2 | semidirect |
| 2. #27133060 | C2 | semidirect |
| 3. #27133048 | C2 | semidirect |
| 4. #27133024 | C2 | semidirect |
| 5. #27132918 | C2 | semidirect |
| 7. #27132895 | C2 | semidirect |
| 8. #27132776 | C2 | semidirect |
| 9. C4×#15690274 | C2 | semidirect |
| 10. #27132620 | C2 | semidirect |
| 11. #441×C191 | C2 | semidirect |
| 109. C191 | #3173 | semidirect |
| 119. #441 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133285 | 2 |
| #27133060 | 2 |
| #27133048 | 2 |
| #27133024 | 2 |
| #27132918 | 2 |
| #27132917 | 2 |
| #27132895 | 2 |
| #27132776 | 2 |
| C4×#15690274 | 2 |
| #27132620 | 2 |
| #441×C191 | 2 |
| #3173 | 191 |